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Whenever someone makes or receives a call on a mobile telephone, a Call Detail Record (CDR) is automatically generated by the operator for billing purposes. CDRs have a wide range of applications beyond billing, from social science to data-driven development. Recently, CDRs have been increasingly used to study human mobility, whose understanding is crucial e.g. for planning efficient transportation infrastructure. A major difficulty in analyzing human mobility using CDR data is that the location of a cell phone user is not recorded continuously but typically only when a call is initiated or a text message is sent. In this paper we address this problem, and develop a method for estimating travel times between cities based on CDRs that relies not on individual trajectories of people, but their collective statistical properties. We apply our method to data from Senegal, released by Sonatel and Orange for the …